Results 1  10
of
126
Geometric and Renormalized Entropy in Conformal Field Theory
 NUCL. PHYS. B
, 1994
"... In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the ..."
Abstract

Cited by 149 (0 self)
 Add to MetaCart
(Show Context)
In statistical physics, useful notions of entropy are defined with respect to some coarse graining procedure over a microscopic model. Here we consider some special problems that arise when the microscopic model is taken to be relativistic quantum field theory. These problems are associated with the existence of an infinite number of degrees of freedom per unit volume. Because of these the microscopic entropy can, and typically does, diverge for sharply localized states. However the difference in the entropy between two such states is better behaved, and for most purposes it is the useful quantity to consider. In particular, a renormalized entropy can be defined as the entropy relative to the ground state. We make these remarks quantitative and precise in a simple model situation: the states of a conformal quantum field theory excited by a moving mirror. From this work, we attempt to draw some lessons concerning the “information problem ” in black hole physics.
An algebraic approach to logarithmic Conformal Field Theory
 LECTURES GIVEN AT THE SCHOOL ON LOGARITHMIC CONFORMAL FIELD THEORY AND ITS APPLICATIONS, IPM
, 2001
"... A comprehensive introduction to logarithmic conformal field theory, using an algebraic point of view, is given. A number of examples are explained in detail, including the c = −2 triplet theory and the k = −4/3 affine su(2) theory. We also give some brief introduction to the work of Zhu. ..."
Abstract

Cited by 107 (3 self)
 Add to MetaCart
A comprehensive introduction to logarithmic conformal field theory, using an algebraic point of view, is given. A number of examples are explained in detail, including the c = −2 triplet theory and the k = −4/3 affine su(2) theory. We also give some brief introduction to the work of Zhu.
K3 surfaces and string duality
"... The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial sp ..."
Abstract

Cited by 86 (14 self)
 Add to MetaCart
(Show Context)
The primary purpose of these lecture notes is to explore the moduli space of type IIA, type IIB, and heterotic string compactified on a K3 surface. The main tool which is invoked is that of string duality. K3 surfaces provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. They also make an almost ubiquitous appearance in the common statements concerning string duality. We review the necessary facts concerning the classical geometry of K3 surfaces that will be needed and then we review “old string theory ” on K3 surfaces in terms of conformal field theory. The type IIA string, the type IIB string, the E8 × E8 heterotic string, and Spin(32)/Z2 heterotic string on a K3 surface are then each analyzed in turn. The discussion is biased in favour of purely geometric notions concerning the K3 surface
Geometric Origin of MontonenOlive Duality
"... Introduction The aim of this note is to show how the celebrated MontonenOlive duality [1] for all N = 4 gauge theories in D = 4 can be derived by geometric engineering in the context of type II strings, where it reduces to Tduality. Even though by now there is a lot of evidence for the Montonen ..."
Abstract

Cited by 33 (0 self)
 Add to MetaCart
Introduction The aim of this note is to show how the celebrated MontonenOlive duality [1] for all N = 4 gauge theories in D = 4 can be derived by geometric engineering in the context of type II strings, where it reduces to Tduality. Even though by now there is a lot of evidence for the MontonenOlive duality (see e.g. [2]) there is no derivation of this duality. Even with the recent advances in our understanding of dynamics of string theory the derivation of this duality is not yet complete. The aim of this note is to fill this gap. The approach we will follow is in the context of type II compactifications and is quite general and provides a unified approach to all gauge groups. Moreover we gain an understanding of how the field theory duality works by relating it to well understood perturbative symmetries (Tdualities) of strings. 1 2. MontonenOlive Duality Let us recall what the MontonenOlive duality is: We consid
Quantum Black Holes, Wall Crossing, and Mock Modular Forms
, 2012
"... We show that the meromorphic Jacobi form that counts the quarterBPS states in N = 4 string theories can be canonically decomposed as a sum of a mock Jacobi form and an AppellLerch sum. The quantum degeneracies of singlecentered black holes are Fourier coefficients of this mock Jacobi form, while ..."
Abstract

Cited by 29 (4 self)
 Add to MetaCart
We show that the meromorphic Jacobi form that counts the quarterBPS states in N = 4 string theories can be canonically decomposed as a sum of a mock Jacobi form and an AppellLerch sum. The quantum degeneracies of singlecentered black holes are Fourier coefficients of this mock Jacobi form, while the AppellLerch sum captures the degeneracies of multicentered black holes which decay upon wallcrossing. The completion of the mock Jacobi form restores the modular symmetries expected from AdS3/CFT2 holography but has a holomorphic anomaly reflecting the noncompactness of the microscopic CFT. For every positive integral value m of the magnetic charge invariant of the black hole, our analysis leads to a special mock Jacobi form of weight two and index m, which we characterize uniquely up to a Jacobi cusp form. This family of special forms and another closely related family of weightone forms contain almost all the known mock modular forms including the mock theta functions of Ramanujan, the generating function of HurwitzKronecker class numbers, the mock modular forms appearing in the Mathieu and Umbral moonshine, as well as an infinite number of new examples.
Conformal field theories, representations and lattice constructions
 Comm. Math. Phys
, 1996
"... An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT’s), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwist ..."
Abstract

Cited by 26 (10 self)
 Add to MetaCart
(Show Context)
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT’s), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and Z2twisted theories, H(Λ) and ˜ H(Λ) respectively, which may be constructed from a suitable even Euclidean lattice Λ. Similarly, one may construct lattices ΛC and ˜ ΛC by analogous constructions from a doublyeven binary code C. In the case when C is selfdual, the corresponding lattices are also. Similarly, H(Λ) and ˜ H(Λ) are selfdual if and only if Λ is. We show that H(ΛC) has a natural “triality” structure, which induces an isomorphism H ( ˜ ΛC) ≡ ˜ H(ΛC) and also a triality structure on ˜H ( ˜ ΛC). For C the Golay code, ˜ ΛC is the Leech lattice, and the triality on ˜ H ( ˜ ΛC) is the symmetry which extends the natural action of (an extension of) Conway’s group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman’s construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of selfdual CFT’s. We find that of the 48 theories H(Λ) and ˜ H(Λ) with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doublyeven selfdual binary code
Analytic calculation of scaling dimensions: tricritical hard squares and critical hard hexagons
, 1991
"... The flnitesize corrections, central charges c and scaling dimensions x of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfled by the commuting row transfer matrices of these la ..."
Abstract

Cited by 26 (4 self)
 Add to MetaCart
(Show Context)
The flnitesize corrections, central charges c and scaling dimensions x of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfled by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtain c = 7=10; x = 3=40; 1=5; 7=8; 6=5 and for hard hexagons we obtain c = 4=5; x = 2=15; 4=5; 17=15; 4=3; 9=5 in accord with the predictions of conformal and modular invariance. 1.
SCALING LIMIT FOR THE INCIPIENT SPANNING CLUSTERS
 FOR: THE IMA VOLUMES IN MATHEMATICS AND ITS APPLICATIONS (SPRINGER{VERLAG)
, 1996
"... Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the direct description of the limiting continuum theory. The result ..."
Abstract

Cited by 25 (3 self)
 Add to MetaCart
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the direct description of the limiting continuum theory. The resulting structure is expected to exhibit strict conformal invariance, and facilitate the mathematical discussion of questions related to universality of critical behavior, conformal invariance, and some relations with a number of field theories.